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The mesosphere lies above the stratosphere and below the thermosphere. Its typical terrestrial temperature decreases upward.

For a representative hydrogen-rich hot Jupiter, increasing altitude lowers pressure, slows collision-driven chemistry, and increases exposure to stellar UV. Three principal regimes follow.

At high pressures, illustratively $P\gtrsim 1$--$10$ bar, collisions and sufficiently high temperature make thermochemical equilibrium a useful approximation. Molecular abundances minimize the free energy subject to elemental conservation. Condensation and atmospheric condensate rainout can remove selected elements from the gas.

At intermediate pressures, illustratively $10^{-3}\lesssim P\lesssim 1$ bar, vertical mixing and horizontal winds can outrun chemical relaxation time. The chemical quench level is defined by ${\tau }_{\mathrm{chem}}\sim {\tau }_{\mathrm{mix}}$; above it, some abundances retain values from a deeper or hotter region. Horizontal chemical quenching similarly occurs when chemical adjustment is slower than advection between the day and night hemispheres.

At low pressures, illustratively $P\lesssim 10^{-3}$ bar, atmospheric photochemistry becomes important: photodissociation and radical reactions change equilibrium abundances and can produce hydrocarbons and atmospheric hazes. At still lower pressures, roughly $10^{-6}$ bar and above in altitude, photoionization and an escaping thermosphere can become important.

These pressures label a representative sketch, not universal interfaces. UV optical depth, stellar spectrum, gravity, metallicity, reaction rates and eddy diffusivity determine the transitions; quenching is species-dependent.

The functional form is not specific to exoplanets. With positive pressure normalization and physical temperature, a square-root exponential atmospheric profile can approximate a monotone interval of the terrestrial atmosphere. An outward-cooling interval, such as part of the troposphere or mesosphere, requires $\alpha >0$. An upward-warming interval, such as part of the stratosphere heated by ultraviolet absorption or the thermosphere heated by high-energy radiation, requires $\alpha <0$.

The local atmospheric lapse rate follows from the ideal gas relation $P=\rho k_{B}T/(\mu m_H)$ and hydrostatic equilibrium:For dry terrestrial air, approximately $\gamma =1.4$ and $\mu \simeq 29$ give the dry-adiabatic lapse rate $g/c_p\simeq 9.8\mathrm{K}\mathrm{k}{\mathrm{m}}^{-1}$. The familiar mean tropospheric value near $6.5\mathrm{K}\mathrm{k}{\mathrm{m}}^{-1}$ is less steep; a local fit must satisfy $\nabla \lesssim 2/7$ to be dry-convectively stable. Moist convection needs the moist parcel thermodynamics instead, and the terrestrial atmosphere is not uniformly dry or chemically homogeneous at all heights.

The squared-logarithm shape cannot reproduce an exactly constant nonzero lapse rate over an arbitrary thick region, all the alternating atmospheric layers, or a finite exactly isothermal region. It is a local parametrization with a fixed sign of the temperature gradient; it has no terrestrial universality.

The terrestrial atmosphere has regions with opposite signs of the atmospheric lapse rate: the troposphere usually cools upward, the stratosphere warms upward through ultraviolet heating, the mesosphere cools, and the thermosphere warms. A monotone atmospheric pressure-temperature profile can approximate one such interval, but cannot describe all their transitions with one fixed branch.